Vertical-cavity surface emitting laser

ABSTRACT

By making use of a vertical cavity surface emitting laser element ( 100 ) in accordance with the present invention, it becomes able to suppress as properly an occurrence of any dislocation therein even in a case where there is formed a DBR mirror onto a substrate ( 1 ), by designing to be set for between an average of strain in a DBR mirror at the lower side thereof ( 2 ) and a layer thickness of such the DBR mirror at the lower side thereof ( 2 ) in reference to a curvature of the substrate ( 1 ) in order to be satisfied a predetermined condition, and then by performing an addition of nitrogen into the DBR mirror at the lower side thereof ( 2 ) with a composition thereof that corresponds to the designed average of strain in the DBR mirror at the lower side thereof ( 2 ) to be set therefor, such as the composition of between 0.028% and 0.390% or the like, in reference to the relationship of between the average of strain in the DBR mirror at the lower side thereof ( 2 ) and an average of the composition of the nitrogen that is included in the DBR mirror at the lower side thereof ( 2 ).

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a vertical cavity surface emitting laser element that comprises: a reflecting mirror of a multilayered film layer at a lower side thereof, that is formed by making use of a periodic structure of between a layer having an index of refraction as higher and a layer having an index of refraction as lower; and a multilayered film layer at an upper side thereof, that is formed by making use of a periodic structure of between a layer having an index of refraction as higher and a layer having an index of refraction as lower.

2. Description of the Related Art

A surface emitting laser element of a vertical cavity type (VC-SEL: referred to as a surface emitting laser element hereinafter) is made use for a variety of sources of light for a usage of an optical communication, such as an optical interconnection or the like, or for a device for a usage of any other applications as a variety thereof (refer to the following Patent Document 1 for instance). Moreover, from such the surface emitting laser element there is emitted a laser light in a vertical direction to a substrate thereof. And then thereby with making use of such the surface emitting laser element, it is able to array other elements with the number as a plurality thereof in two-dimensional on a same substrate as easier comparing to any other laser elements of emission type from end face thereof as conventional. Further, such the surface emitting laser element has a lot of advantages, such as thereby it is possible to perform a laser oscillation with a threshold electrical current as extremely lower and with a power consumption as lower due to a volume of an active layer therein is designed to be as extremely smaller. Furthermore, there is made use of a distributed Bragg reflector (DBR) mirror for a mirror in order to configure a resonator in accordance with such the surface emitting laser element.

Here in a case where there is accumulated a DBR mirror onto a substrate, there is a problem that there is occurred a dislocation therein due to a lattice mismatch for between the substrate and such the DBR mirror thereon, and hence that it cannot help but being decreased a reliability of such the surface emitting laser element thereby. And therefore there is proposed in the past years in order to decrease such the dislocation therein, such as a surface emitting laser element that there is adopted a substrate that there is added indium (In) thereinto and then thereby that there is decreased a curvature of such the substrate and hence that there is decreased an occurrence of the dislocation therein thereby as well (refer to Patent Document 1), or a surface emitting laser element that there is added a nitrogen thereinto and then thereby that there is maintained a lattice match in therebetween (refer to the following Patent Document 2 and the following Patent Document 3), or the like.

[Patent Document 1] Japanese Patent Application Publication No. 2005-252111

[Patent Document 2] Japanese Patent Application Publication No. H10 (1998)-173295

[Patent Document 3] Japanese Patent Application Publication No. H06 (1994)-037355

However, there is a problem with making use of the surface emitting laser element in accordance with Patent Document 1 that it is further difficult as technically to add it into such the substrate as uniformly. Moreover, there is not mentioned as specifically regarding an amount of nitrogen by which it is able to decrease as properly an occurrence of any dislocation in accordance with both of Patent Document 2 and Patent Document 3, though there is mentioned regarding the addition of nitrogen into a material of a semiconductor that is designed to configure a DBR mirror. And hence there is a problem thereby that there is remained a difficulty to perform a production of a surface emitting laser element as a real case thereof in which there is suppressed an occurrence of any dislocation therein.

And therefore an object in accordance with the present invention is to provide a vertical cavity surface emitting laser element by which there is designed to be suppressed an occurrence of any dislocation therein even in a case where there is formed a DBR mirror onto a substrate, and hence that becomes to have a reliability as higher thereby.

SUMMARY OF THE INVENTION

In order to solve each of such the subjects that are mentioned above and in order to accomplish such an objective therefor, a first aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that such the vertical cavity surface emitting laser element comprises: a substrate; a reflecting mirror of a multilayered film layer at a lower side thereof, that is formed on the substrate by making use of a periodic structure of between a layer at a lower side thereof having an index of refraction as higher which is formed by making use of a chemical compound which includes Ga and As, and a layer at a lower side thereof having an index of refraction as lower which is formed by making use of a chemical compound which includes Al and As; an optical resonator which comprises a reflecting mirror of a multilayered film layer at an upper side thereof, that is formed by making use of a periodic structure of between a layer at an upper side thereof having an index of refraction as higher and a layer at an upper side thereof having an index of refraction as lower; and an active layer, that is provided in between the reflecting mirror of the multilayered film layer at the lower side thereof and the reflecting mirror of the multilayered film layer at the upper side thereof, and that generates a light emission, wherein there is included a nitrogen in the reflecting mirror of the multilayered film layer at the lower side thereof, there is designed to be set for between an average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof and a layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof in reference to the following formula (2) for a curvature of the substrate to be satisfied with the following formula (1) in a case where the curvature of the substrate is defined here to be as (C) (μm), the average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (S) (%), a thickness of the substrate is defined to be as (d) (μm), a diameter of the substrate is defined to be as (D) (inch), and the layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (T) (μm), and there is included the nitrogen in the reflecting mirror of the multilayered film layer at the lower side thereof with having a composition which corresponds to the average of strain (S) by designing to be set with making use of the formula (2) in accordance with a relationship between the average of strain and an average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof.

[Formula  (1)] $\begin{matrix} {{C} < {61.5 \times \left( \frac{450}{d} \right)^{2} \times {\left( \frac{D}{3} \right)^{2}\left\lbrack {{Formula}\mspace{14mu} (2)} \right\rbrack}}} & (1) \\ {C = {\frac{\left( {{27.7S} - 1.48} \right)}{0.2} \times \left( \frac{450}{d} \right)^{2} \times \left( \frac{D}{3} \right)^{2} \times T}} & (2) \end{matrix}$

Here the average of strain is defined to be as ((lattice mismatch of the layer at the lower side thereof having the index of refraction as higher that corresponds to the substrate) times (the thickness of the layer at the lower side thereof having the index of refraction as higher)+(lattice mismatch of the layer at the lower side thereof having the index of refraction as lower that corresponds to the substrate) times (the thickness of the layer at the lower side thereof having the index of refraction as lower)) divided by ((the thickness of the layer at the lower side thereof having the index of refraction as higher)+(the thickness of the layer at the lower side thereof having the index of refraction as lower)). Moreover, the average of the composition of the nitrogen is defined here to be as ((a composition rate of the nitrogen in the layer at the lower side thereof having the index of refraction as higher) times (the thickness of the layer at the lower side thereof having the index of refraction as higher)+(a composition rate of the nitrogen in the layer at the lower side thereof having the index of refraction as lower) times (the thickness of the layer at the lower side thereof having the index of refraction as lower)) divided by ((the thickness of the layer at the lower side thereof having the index of refraction as higher)+(the thickness of the layer at the lower side thereof having the index of refraction as lower)). Furthermore, the composition rate of the nitrogen therein is defined here to be as a rate of content regarding any of the elements therein that include nitrogen among all of the elements therein that configure the layer at the lower side thereof having the index of refraction as higher and the layer at the lower side thereof having the index of refraction as lower.

Moreover, a second aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in the first aspect, the relationship between the average of strain and the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is expressed by making use of the following formula (3) in a case where the average of composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is defined to be as (N).

[Formula (3)]

N=−2.4756S+0.3409  (3)

Further, a third aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in either one of the first aspect or the second aspect, there is designed for the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as between 0.028% and 0.390%.

Still further, a fourth aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in the third aspect, there is designed for the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 0.072%.

Still further, a fifth aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in the third aspect, there is designed for the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 0.263%.

Still further, a sixth aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that such the vertical cavity surface emitting laser element further comprises: a substrate; a reflecting mirror of a multilayered film layer at a lower side thereof, that is formed on the substrate by making use of a periodic structure of between a layer at a lower side thereof having an index of refraction as higher which is formed by making use of a chemical compound which includes Ga and As, and a layer at a lower side thereof having an index of refraction as lower which is formed by making use of a chemical compound which includes Al and As; an optical resonator which comprises a reflecting mirror of a multilayered film layer at an upper side thereof, that is formed by making use of a periodic structure of between a layer at an upper side thereof having an index of refraction as higher and a layer at an upper side thereof having an index of refraction as lower; and an active layer, that is provided in between the reflecting mirror of the multilayered film layer at the lower side thereof and the reflecting mirror of the multilayered film layer at the upper side thereof, and that generates a light emission, wherein there is included a phosphorus in the reflecting mirror of the multilayered film layer at the lower side thereof, there is designed to be set for between an average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof and a layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof in reference to the following formula (5) for a curvature of the substrate to be satisfied with the following formula (4) in a case where the curvature of the substrate is defined here to be as (C) (μm), the average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (S) (%), a thickness of the substrate is defined to be as (d) (μm), a diameter of the substrate is defined to be as (D) (inch), and the layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (T) (μm), and there is included the phosphorus in the reflecting mirror of the multilayered film layer at the lower side thereof with having a composition which corresponds to the average of strain (S) by designing to be set with making use of the formula (5) in accordance with a relationship between the average of strain and an average of the composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof.

[Formula  (5)] $\begin{matrix} {C = {\frac{\left( {{27.7S} - 1.48} \right)}{0.2} \times \left( \frac{450}{d} \right)^{2} \times \left( \frac{D}{3} \right)^{2} \times T}} & (5) \end{matrix}$

Here the average of strain is defined to be as ((lattice mismatch of the layer at the lower side thereof having the index of refraction as higher that corresponds to the substrate) times (the thickness of the layer at the lower side thereof having the index of refraction as higher)+(lattice mismatch of the layer at the lower side thereof having the index of refraction as lower that corresponds to the substrate) times (the thickness of the layer at the lower side thereof having the index of refraction as lower)) divided by ((the thickness of the layer at the lower side thereof having the index of refraction as higher)+(the thickness of the layer at the lower side thereof having the index of refraction as lower)). Moreover, the average of the composition of the phosphorus is defined here to be as ((a composition rate of the phosphorus in the layer at the lower side thereof having the index of refraction as higher) times (the thickness of the layer at the lower side thereof having the index of refraction as higher)+(a composition rate of the phosphorus in the layer at the lower side thereof having the index of refraction as lower) times (the thickness of the layer at the lower side thereof having the index of refraction as lower)) divided by ((the thickness of the layer at the lower side thereof having the index of refraction as higher)+(the thickness of the layer at the lower side thereof having the index of refraction as lower)). Further, the composition rate of the phosphorus therein is defined here to be as a rate of content regarding any of the elements therein that include phosphorus among all of the elements therein that configure the layer at the lower side thereof having the index of refraction as higher and the layer at the lower side thereof having the index of refraction as lower.

Still further, a seventh aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in the sixth aspect, the relationship between the average of strain and the average of the composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is expressed by making use of the following formula (6) in a case where the average of composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is defined to be as (P).

[Formula (6)]

P=−14.578S+2.0113  (6)

Still further, an eighth aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in either one of the sixth aspect or the seventh aspect, there is designed for the average of composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as between 0.169% and 2.309%.

Still further, a ninth aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in either one of the sixth aspect or the seventh aspect, there is included the phosphorus in the layer at the lower side thereof having the index of refraction as lower in the reflecting mirror of the multilayered film layer at the lower side thereof, and there is designed for the composition of the phosphorus which is included in the layer at the lower side thereof having the index of refraction as lower to be as between 0.338% and 4.621%.

Still further, a tenth aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in the eighth aspect, there is designed for the average of the composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 0.410%.

Furthermore, an eleventh aspect of a vertical cavity surface emitting laser element in accordance with the present invention is characterized in that regarding such the vertical cavity surface emitting laser element as described in the eighth aspect, there is designed for the average of the composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 1.551%.

And therefore by making use of such the vertical cavity surface emitting laser element in accordance with the present invention, it becomes able to suppress as properly an occurrence of any dislocation therein even in a case where there is formed a DBR mirror onto the substrate, by designing to be set for between the average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof and the layer thickness of such the reflecting mirror of the multilayered film layer at the lower side thereof in reference to the curvature of the substrate in order to be satisfied a predetermined condition therefor, and then by performing an addition of nitrogen into the reflecting mirror of the multilayered film layer at the lower side thereof with the composition thereof that corresponds to the designed average of strain therein to be set therefor, in reference to the relationship of between the average of strain therein and the average of composition of nitrogen that is included in the reflecting mirror of the multilayered film layer at the lower side thereof.

The above and other objects, features, advantages and technical and industrial significance of this invention will be better understood by reading the following detailed description of presently preferred embodiments of the invention, when considered in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view showing a configuration of a vertical cavity surface emitting laser element in accordance with the first embodiment.

FIG. 2 is a cross sectional view showing a cross section from a point of view on a line of II-II as shown in FIG. 1.

FIG. 3 is a graph showing a relation between a Lattice strain in a DBR mirror at a lower side thereof and a dislocation density thereof.

FIG. 4 is a graph showing a relation between an average of strain (an average of Lattice strain) in a DBR mirror at a lower side thereof and an amount of curvature of a substrate.

FIG. 5 is a graph showing a relation between a Lattice strain in a DBR mirror at a lower side thereof and a composition of nitrogen to be added into the DBR mirror.

FIG. 6 is a graph showing a relation between an average of a composition of nitrogen at an inner side of a DBR mirror at a lower side thereof and an amount of curvature of a substrate.

FIG. 7 is a cross sectional view showing a schematic configuration regarding a principal part of a vertical cavity surface emitting laser element in accordance with the second embodiment.

FIG. 8 is a graph showing a relation between a Lattice strain in a DBR mirror at a lower side thereof and a composition of phosphorus to be added into the DBR mirror.

EXPLANATION OF REFERENCE NUMERALS

-   -   K1

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A couple of embodiments in accordance with the present invention will be described in detail below in reference to the drawings. Here the present invention will not be limited by each of such the embodiments. Moreover, there is made use of a same symbol for each of the parts as similar to therebetween. Further, each of the drawings are exemplary shown, and then thereby it is necessary to note here that such a case is different from that of reality respectively, such as a relationship between a thickness of each of the layers therein and a width thereof, or a ratio of between each of the layers therein, or the like. Furthermore, there is included some parts in which there is differed a relationship of dimensions for each other therefrom or a ratio of therebetween for each other therefrom regarding mutual relationship between each of the drawings as well.

The First Embodiment

Here FIG. 1 and FIG. 2 are views for showing a schematic configuration of a principal part of a vertical cavity surface emitting laser element (100) regarding the first embodiment in accordance with the present invention, wherein FIG. 1 is a plan view therefor, meanwhile, FIG. 2 is a cross sectional view for showing a cross section from a point of view on a line of II-II as shown in FIG. 1 on the contrary thereto. And then as shown in such the views, the vertical cavity surface emitting laser element (100) comprises: a substrate (1), such as a substrate of GaAs which has a orientation of plane as (001); a DBR mirror at a lower side thereof (2), that is accumulated onto the substrate (1), and that functions as a reflecting mirror of a multilayered film layer at a lower side thereof; a contact layer of an n type (3) to be accumulated thereunto; an electrode of an n type (4) to be accumulated thereunto; a cladding layer of an n type (5); an active layer (6) to be accumulated thereunto; a cladding layer of a p type (7) to be accumulated thereunto; an electrical current narrowing layer (8) to be accumulated thereunto; a cladding layer of a p type (9) to be accumulated thereunto; a contact layer of a p type (10) to be accumulated thereunto; an electrode of a p type (11) to be accumulated thereunto; and a DBR mirror at an upper side thereof (12), that functions as a reflecting mirror of a multilayered film layer at an upper side thereof. Moreover, there are designed for the cladding layer of the n type (5), the active layer (6) which is accumulated thereunto, the cladding layer of the p type (7) which is accumulated thereunto, the electrical current narrowing layer (8) which is accumulated thereunto and the cladding layer of the p type (9) which is accumulated thereunto to be formed as individual mesa posts, that individually are formed to be as a post shape by making use of such as a process of etching therefor or the like among such the parts therein respectively. Moreover, there may be designed for the DBR mirror at the lower side thereof (2) to be formed onto a buffer layer of GaAs which is accumulated onto the substrate (1).

Further, there is designed for the DBR mirror at the lower side thereof (2) to be formed as a mirror of a multi layered film layer of a semiconductor, in which there are accumulated a layer of GaAs which functions as a layer having an index of refraction as higher and a layer of AlAs or a layer of AlGaAs which functions as a layer having an index of refraction as lower that are assumed to be as one pair, and then there are accumulated such the pairs as a plurality thereof. Still further, there is designed for a thickness of each of the layers that configures the layers of the composite semiconductor in the DBR mirror at the lower side thereof (2) to be as λ/4n (l: a wavelength of emission, n: an index of refraction) respectively. Still further, there is designed for such the DBR mirror at the lower side thereof (2) to be added a nitrogen with a predetermined composition. Furthermore, there is designed to make use of a source of nitrogen by making use of a radio frequency (an RF) plasma in order to introduce nitrogen into each of such the layers which configures the DBR mirror at the lower side thereof (2), and then thereby there is designed to be introduced thereinto as a state of an activated nitrogen.

Moreover, there is designed for the contact layer of the n type (3) to be formed with making use of a material of such as an n-GaAs or the like onto the DBR mirror at the lower side thereof (2). Further, there is designed for the cladding layer of the n type (5) to be formed with making use of a material of such as an n-GaAs or the like onto the contact layer of the n type (3). Still further, there is designed for the cladding layer of the p type (7) to be formed with making use of a material of such as a p-GaAs or the like onto the active layer (6) which will be described in detail later. Still further, there is designed for the cladding layer of the p type (9) to be formed with making use of a material of such as a p-GaAs or the like onto the electrical current narrowing layer (8) which will be described in detail later as well. Furthermore, there is designed for the contact layer of the p type (10) to be formed with making use of a material of such as a p-GaAs or the like onto the cladding layer of the p type (9).

Moreover, there is designed for such the electrical current narrowing layer (8) to be formed onto the cladding layer of the p type (7), and then the same is comprised of an open part (8 a) as the open part for narrowing the electrical current and a layer to be selectively oxidized (8 b). Further, there is designed for such the electrical current narrowing layer (8) to be formed with making use of a layer to be included Al which is comprised of such as an AlAs or the like. Still further, there is designed for such the layer to be selectively oxidized (8 b) to be formed as a ring zonal shape by being oxidized such the layer to be included Al only within a predetermined zone along a face to be accumulated from a peripheral part thereof. Furthermore, such the layer to be selectively oxidized (8 b) has a non-conductivity as electrically, and then the same enhances a density of an electrical current at a part as directly under the open part (8 a) by narrowing the electrical current to be injected from the electrode of the p type (11) and then by focusing into an inner side of such the open part (8 a).

Moreover, the active layer (6) has a multiple quantum well (an MQW) structure of which there are accumulated layers of a composite semiconductor as three layers thereof that is comprised of such as a GaInNAs/GaAs or the like, and then there is emitted a spontaneously emitted light therefrom with having a band of 1.3 μm, by being based on the electrical current that is injected from the electrode of the p type (11) and then that is narrowed by making use of the electrical current narrowing layer (8). Further, there is designed for the layer of GaInNAs therein to function as a quantum well, meanwhile, there is designed for the layer of GaAs therein to function as a barrier layer. Furthermore, there is designed for such the spontaneously emitted light therefrom to be resonated and then to be amplified in a vertical direction to each of the layers that include the active layer (6) at between the DBR mirror at the lower side thereof (2) and the DBR mirror at the upper side thereof (12) that are designed to be as a resonator. And then thereafter there is emitted as a laser light from an upper surface part on the DBR mirror at the upper side thereof (12).

Moreover, there is designed for such the DBR mirror at the upper side thereof (12) to be formed onto the contact layer of the p type (10). Further, there is designed for such the DBR mirror at the upper side thereof (12) to be formed as a mirror of a multi layered film layer of dielectric substance in which there is accumulated a composite layer of dielectric substance as a plurality of pairs that is comprised of such as an SiN/SiO₂ or the like. Still further, there is designed for a thickness of each of the layers therein to be as λ/4n as similar to that in the DBR mirror at the lower side thereof (2). Furthermore, there is designed for such the DBR mirror at the upper side thereof (12) to be performed an accumulation of a multi layered film layer of dielectric substance which has a predetermined number of layers within a zone that includes the mesa post for instance, and then thereafter there is designed therefor to be formed by performing an etching (a process of etching) that is not for a part at right above the open part (8 a) in such the multi layered film layer of dielectric substance but that is for a zone as peripheral thereto.

Moreover, there is designed for such the electrode of the p type (11) to be accumulated onto the contact layer of the p type (10), and then there is designed therefor to be formed as a ring shape for surrounding along the DBR mirror at the upper side thereof (12). Further, there is designed for the electrode of the n type (4) on the contrary thereto to be accumulated onto the cladding layer of the n type (3), and then there is designed therefor to be formed as a letter of C shape for surrounding along an accumulated face on a bottom face part of the mesa post. Still further, there are designed for such the electrode of the p type (11) and the electrode of the n type (4) to be connected as electrically to an external circuit individually which is not shown in any of the figures (such as an electrical current supply circuit or the like), with making use of an electrode of an n type for extraction (13) and an electrode of a p type for extraction (14). Still further, there may be performed the accumulation regarding each of the layers of the semiconductor by making use of a method for accumulating, such as a molecular beam epitaxy (an MBE) or an MBE with a gas source or a chemical beam epitaxy (CBE) or a metalorganic chemical vapor deposition (MOCVD) or the like. Furthermore, it is available to make use of such as a dimethylhydrazine (DMHy) or an ammonia (NH₃) or the like as a raw material for generating nitrogen in a case of making use of the MOCVD therefor.

Here, up to now there has been a problem that there is occurred a dislocation in a case where there is accumulated a DBR mirror at a lower side thereof on a substrate, and hence that it cannot help but being decreased a reliability of a vertical cavity surface emitting laser element thereby. Moreover, such the dislocation therein is caused due to an occurrence of a lattice mismatch for between the substrate and the DBR mirror at the lower side thereof due to a strain to be accumulated at an inner side of such the DBR mirror at the lower side thereof.

So, there is examined regarding a Lattice strain in a DBR mirror at a lower side thereof in which there becomes to be disappeared a dislocation in accordance with the present first embodiment, for which there is performed a production of some samples in which there is changed the Lattice strain in each of the DBR mirrors at the lower side thereof in actual respectively. Here FIG. 3 is a graph for showing a relation of between a Lattice strain in a DBR mirror at a lower side thereof and a dislocation density thereof. And then there is obtained a result as shown in such FIG. 3 by performing the production of some samples that individually have the Lattice strain as different from each other, by changing a lattice constant with varying a composition of Al in a layer of AlGaAs in actual among the composition film layers that configure the DBR mirrors at the lower side thereof respectively, and then by evaluating with being based on each of the results that there is performed the measurements of the dislocation density that is occurred in each of such the samples respectively. Moreover, the dislocation density thereof as mentioned above is defined here to be as the number of an aggregate (to be regarded) of the arrays of the lattice defects due to the lattice mismatch per one square millimeter which is observed and confirmed at a period of an observation for a surface thereof by making use of a microscope of the Nomarski type on which there is attached a prism of the Nomarski type onto an optical microscope.

Further, there is obtained the dislocation density thereof as high as approximately 630 (mm⁻²) in a case where the Lattice strain in the DBR mirror at the lower side thereof is approximately 0.14% as shown in FIG. 3. And then the lower there is decreased the Lattice strain in the DBR mirror at the lower side thereof, the lower there becomes to be decreased such the dislocation density thereof. That is to say, it is found out that there is having a relation as proportional to therebetween that the lower there is decreased the Lattice strain therein, the lower there becomes to be decreased such the dislocation density thereof, and more specifically that there is having a relation as expressed in the following formula (7). Still further, there is defined for an average of strain in the DBR mirror at the lower side thereof to be as (S) (%) in accordance with the formula (7), and there is defined for the dislocation density thereof that is occurred therein to be as (H) (mm⁻²) therein.

[Formula (7)]

H=55120S−6966.7  (7)

Still further, it is considered in accordance with the formula (7) that there becomes the dislocation density thereof to be as zero (mm⁻²) in a case where there is designed for the Lattice strain in the DBR mirror at the lower side thereof to be as 0.126% which is arrowed with making use of the arrow (Y1) as shown in FIG. 3. Still further, it is considered that there becomes to be disappeared such the dislocation therein by designing for the Lattice strain therein to be as not higher than 0.126%, because there is having the relation as proportional to therebetween that the lower there is decreased the Lattice strain in the DBR mirror at the lower side thereof, the lower there becomes to be decreased such the dislocation density thereof. That is to say, it is considered that a value of an upper limit is determined here to be as 0.126% regarding the Lattice strain in the DBR mirror at the lower side thereof for a case where there becomes to be disappeared the dislocation in the DBR mirror at the lower side thereof. Furthermore, it becomes to be clear in accordance with the result as shown in FIG. 3 that the value of the upper limit is determined to be as 0.126% regarding the Lattice strain therein for a case where there becomes to be disappeared the dislocation therein.

Next, there is examined as described below regarding a value of a lower limit for a Lattice strain in a DBR mirror at a lower side thereof for a case where there becomes to be disappeared the dislocation therein. Here, there is a relation in general that the larger a curvature of a substrate is, the larger there becomes for a Lattice strain in a DBR mirror at a lower side thereof to be as well. While, there is a relation that the smaller the curvature of the substrate is, the smaller there becomes for the Lattice strain in the DBR mirror at the lower side thereof to be on the contrary thereto. That is to say, there is having the relation that there is varied the Lattice strain in the DBR mirror at the lower side thereof with corresponding to an amount of the curvature of the substrate. And then thereby there is examined a relation of between such the amount of the curvature of the substrate and the Lattice strain in the DBR mirror at the lower side thereof in accordance with the present first embodiment. And hence there is performed an evaluation of the value of the lower limit regarding the Lattice strain in the DBR mirror at the lower side thereof for a case where there becomes to be disappeared the dislocation therein, by making use of such the obtained relation of between the amount of the curvature of the substrate and the Lattice strain in the DBR mirror at the lower side thereof.

Here, FIG. 4 is a graph for showing a relation of between a Lattice strain in a DBR mirror at a lower side thereof and an amount of curvature of a substrate. Moreover, the curvature of the substrate is defined here to be as a maximum difference of between a center of the substrate and a height of an edge of the substrate. And then there is performed a conversion from such the amount of the curvature thereof into an amount of the curvature thereof per one pair of the DBR mirrors at the lower side thereof that is indicated on the horizontal axis in FIG. 4. Further, there is shown such the horizontal axis in FIG. 4 to be as an average value of the Lattice strain in the DBR mirror at the lower side thereof. Still further, there is performed a production in actual in accordance with FIG. 4: by forming each of the samples (S1) that individually comprises the DBR mirror at the lower side thereof in which there is designed for each of the Lattice strains to be individually changed by being varied each of the compositions of the Al in the individual layers of AlGaAs respectively, onto the individual substrates that individually have the thicknesses of approximately 450 μm respectively; by forming each of the samples (S2) that individually comprises the DBR mirror at the lower side thereof in which there is designed for each of the Lattice strains to be individually changed by being varied each of the compositions of nitrogen to be added into the individual layers of AlAs respectively, onto the individual substrates that individually have the thicknesses of approximately 450 μm respectively; by forming each of the samples (S3) that individually comprises the DBR mirror at the lower side thereof in which there is designed for each of the Lattice strains to be individually changed by being varied each of the compositions of nitrogen to be added into the individual layers of AlAs respectively, onto the individual substrates that individually have the thicknesses of approximately 625 μm respectively; and by forming each of the samples (S4) that individually comprises the DBR mirror at the lower side thereof in which there is designed for each of the Lattice strains to be individually changed by being varied each of the compositions of carbon to be added into the individual layers of AlAs respectively, onto the individual substrates that individually have the thicknesses of approximately 625 μm respectively. And then thereafter there is performed each of measurements of an amount of the curvature regarding each of such the substrates for the individual samples respectively. Still further, there is performed an evaluation therefor with being based on each of the results thereof by performing a conversion into an amount of the curvature thereof per one pair of the DBR mirrors at the lower side thereof. Still further, such the nitrogen and such the carbon that individually have the atomic radiuses as smaller comparing to that of As respectively, that individually are added into the corresponding layers of AlAs that individually configure the corresponding layers having the corresponding indexes of refraction as lower in the corresponding DBR mirrors at the lower side thereof. And then thereby there becomes to be decreased the lattice constant of each of the layers of AlAs by being inserted either one of such the atoms into a site of As respectively. And hence both of such the atoms become to have a function by which there becomes to be reduced the Lattice strain in the whole of the DBR mirror at the lower side thereof that comprises such the layer of AlAs as the layer having the index of refraction as lower.

Still further, regarding each of the straight lines as shown in FIG. 4, the straight line (R2) therein indicates a relation of between the Lattice strain in the DBR mirror at the lower side thereof and the amount of the curvature of the substrate in the case of the thickness of the substrate as approximately 450 μm, meanwhile, the straight line (R3) therein indicates a relation of between the Lattice strain therein and the amount of the curvature of the substrate in the case of the thickness of the substrate as approximately 625 μm on the contrary thereto. And then as shown with making use of such the straight lines (R2) and (R3) in accordance with FIG. 4, there is obtained a relation of between the Lattice strain in the DBR mirror at the lower side thereof and the amount of the curvature of the substrate for both of the cases of the thickness of the substrate as approximately 450 μm and that thereof as approximately 625 μm respectively, that the lower there is decreased the Lattice strain in the DBR mirror at the lower side thereof, the lower there becomes to be decreased the amount of the curvature of the substrate as proportional thereto respectively. That is to say, there is determined the proportional connection of between the Lattice strain in the DBR mirror at the lower side thereof and the amount of the curvature of the substrate, that the lower there is decreased the Lattice strain therein, the lower there becomes to be decreased the amount of the curvature of the substrate.

And then as shown in FIG. 4, the Lattice strain in the DBR mirror at the lower side thereof is determined to be as approximately 0.053% for the amount of the curvature of the substrate to be as zero in both of the cases of the thickness of the substrate as approximately 450 μm and that thereof as approximately 625 μm respectively. That is to say, it is found out in accordance with FIG. 4 that there is not become zero for the amount of the curvature of the substrate in a case where there is designed for the Lattice strain in the DBR mirror at the lower side thereof to be as zero percent, but there becomes to be zero for such the amount of the curvature of the substrate in the case where there is designed for the Lattice strain in the DBR mirror at the lower side thereof to be as approximately 0.053%. And then it is considered that there is increased or decreased such the amount of the curvature of the substrate as proportional to the Lattice strain in the DBR mirror at the lower side thereof with the Lattice strain of approximately 0.053% therein to be as a center therefor, because there is determined the proportional connection of between the Lattice strain in the DBR mirror at the lower side thereof and the amount of the curvature of the substrate for both of the cases of the thickness of the substrate as approximately 450 μm and that thereof as approximately 625 μm, that is described above.

Still further, an amount of a curvature of the substrate indicates a positive value as shown in FIG. 4, that corresponds to the value of the upper limit as 0.126% for the Lattice strain in the DBR mirror at the lower side thereof at which the dislocation therein becomes to be disappeared that is evaluated in accordance with FIG. 3. And then thereby the value of the upper limit as 0.126% for the Lattice strain in the DBR mirror at the lower side thereof at which the dislocation therein becomes to be disappeared corresponds to an amount of a curvature thereof in a case where there is curved such a substrate in a positive direction, that is to say, in a case where there becomes to be a convex shape in a direction of the accumulation onto the substrate. Still further, it is found out in accordance with FIG. 3 that the lower there is decreased the Lattice strain in the DBR mirror at the lower side thereof, the lower there becomes to be decreased the amount of the dislocation density thereof. Still further, the lower there is decreased the amount of the curvature of the substrate, the lower there becomes to be decreased the Lattice strain in the DBR mirror at the lower side thereof as proportional thereto as well. And then thereby it can be considered as shown in FIG. 4 that there is occurred a dislocation therein in the case where an amount of the curvature of the substrate is larger comparing to the amount of the curvature thereof that corresponds to the Lattice strain therein for the value of the upper limit as 0.126%, and that there is not occurred any dislocation therein in the case where an amount of the curvature of the substrate is smaller comparing to the amount of the curvature thereof that corresponds to the Lattice strain therein for the value of the upper limit as 0.126% on the contrary thereto. That is to say, it can be considered that the amount of the curvature thereof that corresponds to the Lattice strain therein for the value of the upper limit as 0.126% is assumed to be as a value of an upper limit for the amount of the curvature of the substrate at which there is not occurred any dislocation therein.

Still further, the amount of the curvature thereof that corresponds to the Lattice strain therein for the value of the upper limit as 0.126% is determined to be as approximately 1.8 (μm/period) in the case where the thickness of the substrate is 450 μm, meanwhile, the same is determined to be as approximately 1.0 (μm/period) in the case where the thickness of the substrate is 625 μm on the contrary thereto, and then both of the amounts thereof individually correspond to the amount of the curvature in the cases where each of the substrates are curved in the positive direction respectively. Here, any of such the substrates may be curved not only in the positive direction but also in a negative direction which is a reversed direction to the positive direction (the case where there becomes to be a convex shape to an opposite side for the direction to accumulate the layers onto the substrate). And then it cannot help but being appeared a dislocation in a case where a substrate is curved in the negative direction, because the larger there is curved such the substrate in the negative direction, the larger there becomes to be increased in the negative direction for an amount of strain of a lattice therein.

And then thereby it can be considered that it cannot help but being occurred the dislocation in the case where the substrate is curved in the negative direction, that is caused by the Lattice strain therein with a tendency as similar to the case where the substrate is curved in the positive direction. That is to say, it can be considered that there becomes to be occurred a dislocation in a case where there is curved a substrate in the negative direction with an amount of the curvature as larger comparing to the amount of the curvature which corresponds to the Lattice strain therein for the value of the upper limit as 0.126%. Still further, it can be considered that there becomes not to be occurred any dislocation in a case where there is curved a substrate in the negative direction with an amount of the curvature as smaller comparing to the amount of the curvature which corresponds to the Lattice strain therein for the value of the upper limit as 0.126% on the contrary thereto. That is to say, it can be considered that a value as negative for the amount of the curvature thereof that corresponds to the Lattice strain therein for the value of the upper limit as 0.126% is assumed to be as a value of a lower limit for the amount of the curvature of the substrate at which there is not occurred any dislocation therein. Still further, there becomes to be as approximately −1.8 (μm/period) for the value of the lower limit regarding the amount of the curvature of the substrate at which there is not occurred any dislocation therein in the case where the thickness of the substrate is 450 μm as more specifically thereto, meanwhile, there becomes to be as approximately −1.0 (μm/period) for the value of the lower limit regarding the amount of the curvature of the substrate at which there is not occurred any dislocation therein in the case where the thickness of the substrate is 625 μm on the contrary thereto.

And then as shown in FIG. 4, there is having the proportional connection of between the amount of the curvature of the substrate and the Lattice strain therein for such the amount of the curvature of the substrate to become as zero in a case where the Lattice strain therein is assumed to be as approximately 0.053%. And then thereby it is able to perform an evaluation of a value of a lower limit for the Lattice strain in the DBR mirror at the lower side thereof with corresponding to the value of the lower limit regarding the amount of the curvature of the substrate at which there is not occurred any dislocation therein and with being based on the relation of between the amount of the curvature of the substrate and the Lattice strain in the DBR mirror at the lower side thereof as shown in FIG. 4. And then as shown in FIG. 4, because there is determined for the value of the lower limit regarding the amount of the curvature of the substrate in the case where the thickness of the substrate is 450 μm to be as approximately −1.8 (μm/period) as more specifically thereto, it becomes able to perform the evaluation of the value of the lower limit for the Lattice strain in the DBR mirror at the lower side thereof to be as approximately −0.020% for instance.

Still further, such the relation of between the amount of the curvature of the substrate and the Lattice strain in the DBR mirror at the lower side thereof is different from each other with depending on the thickness of the substrate as shown in FIG. 4. Still further, there is varied such the amount of the curvature of the substrate with depending on a diameter of the substrate as well. While, there is shown the curvature of the substrates as one pair thereof that configure the DBR mirror in accordance with FIG. 4 on the contrary thereto. And then thereby there becomes to be varied such the amount of the curvature of the substrate in a case where there is performed a conversion into a total of the individual thicknesses of the layers for all of the pairs of the DBR mirror, that is to say, a conversion into a total thickness of the film layers of the DBR mirror.

And then thereby with being based on the relation of therebetween as shown in FIG. 4, there is performed an evaluation for the following formula (8) with taking into consideration of the thickness of the substrate, the diameter of the substrate and the total thickness of the film layers of the DBR mirror, that expresses the relation of between the amount of the curvature of the substrate which is due to the DBR mirror and the amount of the Lattice strain in such the DBR mirror. Still further, there is assumed the amount of the curvature of the substrate to be as (C) (μm) in accordance with the formula (8), there is assumed the average of strain in the DBR mirror at the lower side thereof to be as (S) (%) therein, there is assumed the thickness of the substrate to be as (d) (μm) therein, there is assumed the diameter of the substrate to be as (D) (inch) therein, and there is assumed the layer thickness of the DBR mirror at the lower side thereof to be as (T) (μm) therein as well.

[Formula  (8)] $\begin{matrix} {C = {\frac{\left( {{27.7S} - 1.48} \right)}{0.2} \times \left( \frac{450}{d} \right)^{2} \times \left( \frac{D}{3} \right)^{2} \times T}} & (8) \end{matrix}$

And then as substituting the thickness of the substrate as 450 μm and the diameter of the substrate as 3 inches and the total thickness of the film layers of the DBR mirror as 6.09 μm into the formula (8) regarding the sample that is produced in actual therefor, there is performed the evaluation for the amount of the curvature of the substrate (C) to be as 59.3 μm that corresponds to the Lattice strain therein for the value of the upper limit as 0.126% at which there becomes to be disappeared any dislocation therein. Still further, it can be determined for a range of the amount of the curvature of the substrate (C) for which there is not occurred any dislocation in such the sample to be as −59.3 μm<C<61.5 μm, as the substrate may be curved not only in the positive direction but also in the negative direction that is described above. Still further, it is able to reassume the amount of the curvature of the substrate (C) for which there is not occurred any dislocation therein here to be as the following formula (9) in a case where there is taken into consideration of the thickness of the substrate and the diameter of the substrate because there is occurred a variation of the amount of the curvature of the substrate for which there is not occurred any dislocation therein due to the thickness of the substrate and the diameter of the substrate as well. Furthermore, there is assumed the amount of the curvature of the substrate to be as (C) (μm) in accordance with the formula (9) as similar to that in accordance with the formula (8), there is assumed the thickness of the substrate to be as (d) (μm) therein, and there is assumed the diameter of the substrate to be as (D) (inch) therein as well.

[Formula  (9)] $\begin{matrix} {{C} < {61.5 \times \left( \frac{450}{d} \right)^{2} \times \left( \frac{D}{3} \right)^{2}}} & (9) \end{matrix}$

And therefore in accordance with the first embodiment it becomes able to design the amount of the curvature of the substrate (C) for which there is not occurred any dislocation therein. And then thereby there is designed the Lattice strain in the DBR mirror at the lower side thereof and the total thickness of the film layers in such the DBR mirror at the lower side thereof by making use of the formula (8) that is mentioned above, for the amount of the curvature of the substrate (C) to be satisfied with the formula (9). And then as a result therefrom in accordance with the present first embodiment, it becomes able to design as properly the strain (Lattice strain) in the DBR mirror at the lower side thereof for which there is not occurred any dislocation therein and the total thickness of the film layers in such the DBR mirror at the lower side thereof.

Here in the case of the sample in actual that the thickness of the substrate therein is determined to be as approximately 450 μm and the diameter of such the substrate therein is determined to be as approximately 3 inches for instance, the range of the amount of the curvature of the substrate (C) for which there is not occurred any dislocation therein is determined to be as −61.5 μm<C<61.5 μm that is mentioned above. And then in a case where there is assumed the total thickness of the film layers in the DBR mirror at the lower side thereof to be as approximately 6.09 μm, it becomes able to perform an evaluation for a range of the Lattice strain (S) in such the DBR mirror at the lower side thereof to be as −0.020%<S<0.126%, that satisfies such the range of the amount of the curvature of the substrate (C), with making use of the formula (8). And therefore it becomes able to suppress the occurrence of any dislocation therein by performing a control of the Lattice strain in such the DBR mirror at the lower side thereof to be within the range of higher than −0.020% but lower than 0.126% thereby in such the case thereof.

Next, a designing of a Lattice strain in a DBR mirror at a lower side thereof will be described in detail below, in order to suppress an occurrence of a dislocation therein. Here it is possible to perform a control of such the Lattice strain in the DBR mirror at the lower side thereof by making use of an amount of addition of an element to be added into a site of arsenic (As) in place of the constituent element therefor. And then by adding nitrogen with a predetermined composition thereof into a layer having an index of refraction as lower or into a layer having an index of refraction as higher which configure the DBR mirror at the lower side thereof as more specifically thereto, there is performed the control of the Lattice strain in the DBR mirror at the lower side thereof in order to design for such the Lattice strain therein to satisfy an amount of a curvature of a substrate at where there is no occurrence of any dislocation therein. Moreover, a nitrogen has an atomic radius as smaller comparing to that of an As. And then thereby there becomes to be decreased the lattice constant of such as a layer of AlAs or the like by performing an addition of nitrogen into the site of As in such as the layer of AlAs or the like which configures the layer having the index of refraction as lower in the DBR mirror at the lower side thereof (2). And hence it becomes able to design for the Lattice strain in total of such the DBR mirror at the lower side thereof to be as smaller thereby. Further, there becomes to be decreased thereby the lattice constant of a layer of GaAs in a case where there is performed the addition of nitrogen into a site of As in the layer of GaAs which configures the layer having the index of refraction as higher in the DBR mirror at the lower side thereof (2) as well as needless to say. And hence it becomes able to design for the Lattice strain in total of such the DBR mirror at the lower side thereof to be as smaller thereby as well.

Still further, it is able to perform an evaluation as theoretically regarding a relation of between the composition of nitrogen to be added into such the DBR mirror at the lower side thereof and the Lattice strain in such the DBR mirror at the lower side thereof. Here there is shown in FIG. 5 as more specifically thereto regarding such the relation of between a Lattice strain in a DBR mirror at a lower side thereof and a composition of nitrogen to be added into such the DBR mirror. Moreover, there is shown in accordance with FIG. 5 regarding a case where there is performed an arithmetic execution of the Lattice strain in the DBR mirror at the lower side thereof in a case where there is performed the individual additions of nitrogen that individually have the compositions into the layers of AlAs which configure the layer having the index of refraction as lower in the DBR mirror at the lower side thereof (2), and then where there is made an estimation of an average of the composition of the nitrogen at an inner side of the DBR mirror at the lower side thereof by making use of a ratio of between a thickness of the layer at the lower side thereof having the index of refraction as higher and a thickness of the layer at the lower side thereof having the index of refraction as lower.

Further, there is having a proportional connection as theoretically for between the Lattice strain in the DBR mirror at the lower side thereof and the average of the composition of the nitrogen at the inner side of such the DBR mirror at the lower side thereof as shown by making use of a straight line (R4) in FIG. 5, and then thereby it is able to express such the relation thereof by making use of the following formula (10). Still further, there is defined for an average of strain (an average of Lattice strain) in a DBR mirror at the lower side thereof in accordance with the formula (10) here to be as (S) (%), and there is defined for an average of a composition of nitrogen at an inner side of the DBR mirror at the lower side thereof therein here to be as (N) (%).

[Formula (10)]

N=−2.4756S+0.3409  (10)

Still further, there is designed a total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof and the Lattice strain therein in accordance with the first embodiment by making use of the formula (8) which is expressed above, for the amount of the curvature in the substrate (C) in order to satisfy the formula (9) that is expressed above and that is the condition where there is not occurred any dislocation. Furthermore, there is designed for the nitrogen in accordance with the first embodiment to be included in the DBR mirror at the lower side thereof as uniformly in accordance with the formula (10) that is expressed above with a composition that corresponds to the average strain in the DBR mirror at the lower side thereof which is designed to be set by making use of the formula (8) which is expressed above. And therefore it becomes able to suppress the occurrence of any dislocation therein in accordance with the first embodiment by designing the average of composition of nitrogen that is included in the DBR mirror at the lower side thereof by making use of the formula (8) through the formula (10) that are expressed above.

Here in a case where there is selected a sample substrate in actual in which a thickness of the substrate is determined to be as approximately 450 μm and a diameter of the substrate is determined to be as approximately 3 inches for instance, there becomes to be performed an evaluation for a range of the amount of the curvature of the substrate (C) at which there is not occurred any dislocation therein to be as −61.5 μm<C<61.5 μm by making use of the formula (9) that is expressed above. And then thereby in a case where there is further designed for a total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof to be as approximately 6.09 μm for instance, there becomes to be performed an evaluation for a range of the Lattice strain (S) to be as −0.020%<S<0.126% in order to satisfy such the amount of the curvature of the substrate (C) by making use of the formula (8) that is expressed above. And hence it becomes able to perform an evaluation for the average of composition of the nitrogen in the DBR mirror at the lower side thereof to be as higher than 0.028% but lower than 0.390% by making use of the formula (10) which is expressed above, that corresponds to the above mentioned range of the Lattice strain (S) in such the DBR mirror therein. Still further, it becomes able to suppress the occurrence of any dislocation therein in accordance with the first embodiment by performing the addition of nitrogen into the DBR mirror at the lower side thereof (2) as uniformly within such the range of higher than 0.028% but lower than 0.390%. Furthermore, it may be available to perform the addition of nitrogen into the layer of AlAs that configures the layer having the index of refraction as lower in the DBR mirror at the lower side thereof (2) within a range of higher than 0.056% but lower than 0.778% for instance, in order to perform the addition of nitrogen as uniformly into the DBR mirror at the lower side thereof (2) within such the above mentioned range of higher than 0.028% but lower than 0.390%.

And therefore it becomes possible in accordance with the first embodiment to realize the vertical cavity surface emitting laser element that there is designed as properly for suppressing the occurrence of any dislocation therein and then that has the reliability as higher, by designing to be set the total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof and the Lattice strain therein by making use of the formula (8) which is expressed above, for the amount of the curvature in the substrate (C) in order to satisfy the formula (9) that is expressed above and that is the condition where there is not occurred any dislocation therein, and then by performing the addition of nitrogen into the DBR mirror at the lower side thereof with the composition thereof that corresponds to the average of strain in the DBR mirror at the lower side thereof which is designed to be set by making use of the formula (8) that is expressed above. Moreover, in accordance with the present first embodiment in particular, it becomes available to control as simply the amount of the addition of nitrogen to be added into the material of a semiconductor that configures the DBR mirror therein. And then thereby it becomes able to realize as simply such the vertical cavity surface emitting laser element that there is designed as properly for suppressing the occurrence of any dislocation therein and then that has the reliability as higher.

And here there is performed a production of a vertical cavity surface emitting laser element in actual for which there is designed to be set a total of the layer thicknesses of the film layers in a DBR mirror at a lower side thereof and a Lattice strain therein by making use of the formula (8) which is expressed above in order to satisfy the formula (9) that is expressed above, and then there is examined whether or not being occurred any dislocation therein. And then in a case where there is made use of a sample substrate in which a thickness of the substrate is determined to be as approximately 450 μm and a diameter of the substrate is determined to be as approximately 3 inches, where there are designed to be accumulated a layer of GaAs (93 nm approximately) thereunto and then a layer of AlAs (110 nm approximately) thereunto as a DBR mirror at a lower side thereof with 30 pairs thereof in order to obtain a total of the layer thicknesses of such the film layers therein to be as approximately 6.09 μm, and where there is designed to be performed the addition of nitrogen into such the individual layers of AlAs to be as 0.14% in order to obtain the Lattice strain therein to be as 0.083% for instance, there becomes to be obtained for an amount of the curvature of the substrate to be as 4.94 μm that satisfies the formula (9), and hence there becomes not to be occurred thereby any dislocation therein. Moreover, in another case where there is made use of another sample substrate in which a thickness of the substrate is determined to be as approximately 625 μm and a diameter of the substrate is determined to be as approximately 3 inches, where there are designed to be accumulated a layer of GaAs (93 nm approximately) thereunto and then a layer of AlAs (110 nm approximately) thereunto as another DBR mirror at a lower side thereof with 30 pairs thereof in order to obtain a total of the layer thicknesses of such the film layers therein to be as approximately 6.09 μm, and where there is designed to be performed the addition of nitrogen into such the individual layers of AlAs to be as 0.14% in order to obtain the Lattice strain therein to be as 0.083% for instance, there becomes to be obtained for an amount of the curvature of the substrate to be as 12.93 μm that satisfies the formula (9), and hence there becomes not to be occurred thereby any dislocation therein.

Further, in another case on the contrary thereto where there is made use of another sample substrate in which a thickness of the substrate is determined to be as approximately 450 μm and a diameter of the substrate is determined to be as approximately 3 inches, where there are designed to be accumulated a layer of GaAs (93 nm approximately) thereunto and then a layer of AlAs (110 nm approximately) thereunto as another DBR mirror at a lower side thereof with 30 pairs thereof in order to obtain a total of the layer thicknesses of such the film layers therein to be as approximately 6.10 μm, and where there is designed not to be performed any addition of nitrogen at all into such the individual layers of AlAs and then thereby there is obtained the Lattice strain in the DBR mirror at a lower side thereof to be as 0.138% which is higher than the value of the upper limit therefor as 0.126% for instance, it cannot help but being obtained for an amount of the curvature of the substrate to be as 1.45 μm that does not satisfy the value in accordance with the formula (9), and hence there becomes to be occurred thereby some dislocations therein. Furthermore, there is determined for each of the wavelengths of the individual lights that are emitted therefrom to be as approximately 1270 nm respectively.

And therefore there becomes to be examined in accordance therewith in actual that it becomes able to suppress the occurrence of any dislocation in the vertical cavity surface emitting laser element by designing to be set the total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof and the Lattice strain therein by making use of the formula (8) which is expressed above, for the amount of the curvature of the substrate (C) in order to satisfy the formula (9) that is expressed above and that is the condition where there is not occurred any dislocation therein, and then by performing the addition of nitrogen into such the DBR mirror at the lower side thereof by making use of the formula (10) which is expressed above with the composition thereof that corresponds to the average of strain in such the DBR mirror at the lower side thereof which is designed to be set by making use of the formula (8) that is expressed above.

Moreover, it may be available in accordance with the present first embodiment to perform further the control of the amount of nitrogen to be added into the DBR mirror at the lower side thereof as well, by taking into consideration of an amount of the curvature of the substrate that increases due to a process of an accumulation of an active layer onto such the DBR mirror at the lower side thereof.

And then in a case where there is accumulated an active layer of a compressive strain onto a DBR mirror at a lower side thereof for instance, there becomes to be further increased as approximately 15 μm for the amount of the curvature of the substrate thereby. Further, there are designed for the thickness of the substrate and the diameter of the substrate to be determined as a specification of a product on the contrary thereto, and then thereby there are a lot of cases where it is not able to decrease the total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof in order to ensure a rate of reflectance thereof. And therefore it becomes to be required thereby to design for the Lattice strain in the DBR mirror at a lower side thereof to be set by which it becomes able to suppress the occurrence of any dislocation therein by taking into further consideration of an amount of the curvature of the substrate that increases due to the process of the accumulation of the active layer thereunto in such the case thereof.

Still further, there is designed to be performed an evaluation for a Lattice strain (S₁) which corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto as more specifically thereto, by performing an arithmetic execution that will be expressed below in reference to all of the elements in accordance with the Lattice strain (S) in making use of the formula (8) which is expressed above.

(27.7S ₀−1.48)/0.2T=(27.7S ₁−1.48)/0.2T −15.

And in accordance with such the above expressed formula, as substituting −0.020% into (S₀) therein for the value of the lower limit for the Lattice strain therein and as substituting 6.09 μm into (T) therein, for the case where there is not taken into consideration of the accumulation of any of the active layers thereunto at all, it becomes able to obtain 0.640% for the Lattice strain (S₁) therein which corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto. And hence it becomes to be clear thereby that a value of the lower limit for the Lattice strain therein becomes to be as 0.072%, that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto. Moreover, there becomes to be as 0.072% by making use of the formula (10) for an average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof which corresponds to 0.072% as the value of the lower limit for the Lattice strain therein that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto. Further, the value of the upper limit for the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof at which there is not occurred any dislocation therein is here 0.390% that is performed the evaluation as above. And then thereby in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (2), it becomes to be required for the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof to be designed as between 0.072% and 0.390% in order to suppress the occurrence of any dislocation therein. That is to say, in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (2), it becomes to be required for the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof to be designed as not lower than 0.072% in order to suppress the occurrence of any dislocation therein. Still further, regarding a condition for dislocation free in a case where there is designed to be performed an accumulation of an active layer of a tensile strain thereunto, the strain of the DBR becomes to be dominant therein, and hence there becomes not to be occurred any variation thereby regarding the value of the lower limit for the composition thereof.

Still further, it may be available in accordance with the present first embodiment to perform further the control of the amount of nitrogen to be added into the DBR mirror at the lower side thereof as well, by taking into consideration of an amount of the curvature of the substrate that increases due to a further process of an accumulation of a DBR mirror at an upper side thereof onto the active layer therein later.

And then in a case where there is performed an accumulation of an active layer onto a DBR mirror at a lower side thereof and then where there is performed an accumulation of a DBR mirror at an upper side thereof onto such the active layer therein for instance, there becomes to be increased as approximately 15 μm for the amount of the curvature of the substrate due to such the accumulation of the active layer thereunto, and there becomes to be further increased as approximately 65 μm therefor due to such the accumulation of the DBR mirror at the upper side thereof thereunto as well. That is to say, there becomes to be increased as approximately 80 μm for the amount of the curvature of the substrate in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof and then where there is performed the accumulation of the DBR mirror at the upper side thereof onto such the active layer therein. Still further, there is designed to be performed an evaluation for a Lattice strain (S₂) which corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto and due to the accumulation of the DBR mirror at the upper side thereof thereunto, by performing an arithmetic execution that will be expressed below in reference to all of the elements in accordance with the Lattice strain (S) in making use of the formula (8) which is expressed above, in order to design for the Lattice strain therein to be set by which it becomes able to suppress the occurrence of any dislocation therein by taking into further consideration of the amount of the curvature of the substrate that increases in such the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof and then where there is performed the accumulation of the DBR mirror at the upper side thereof onto such the active layer therein.

(27.7S ₀−1.48)/0.2T=(27.7S ₂−1.48)/0.2T −80.

And in accordance with such the above expressed formula, as substituting −0.020% into (S₀) therein for the value of the lower limit for the Lattice strain therein and as substituting 6.09 μm into (T) therein, for the case where there is not taken into consideration of the accumulation of any of the active layers thereunto at all, it becomes able to obtain 0.263% for the Lattice strain (S₁) therein which corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto and due to the accumulation of the DBR mirror at the upper side thereof thereunto. And hence it becomes to be clear thereby that a value of the lower limit for the Lattice strain therein becomes to be as 0.263%, that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto and due to the accumulation of the DBR mirror at the upper side thereof thereunto. Still further, there becomes to be as 0.263% by making use of the formula (10) for an average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof which corresponds to 0.263% as the value of the lower limit for the Lattice strain therein that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto and due to the accumulation of the DBR mirror at the upper side thereof thereunto. Still further, the value of the upper limit for the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof at which there is not occurred any dislocation therein is here 0.390% that is performed the evaluation as above. And then thereby in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (2) and then there is performed the accumulation of the DBR mirror at the upper side thereof thereunto, it becomes to be required for the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof to be designed as between 0.263% but and 0.390% in order to suppress the occurrence of any dislocation therein. That is to say, in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (2) and then there is performed the accumulation of the DBR mirror at the upper side thereof thereunto, it becomes to be required for the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof to be designed as not lower than 0.263% in order to suppress the occurrence of any dislocation therein.

Still further, there is shown in FIG. 6 regarding a result of the evaluation as experimentally for a relation of between an average of a composition of nitrogen at an inner side of a DBR mirror at a lower side thereof and an amount of curvature of a substrate. Still further, a straight line (R5) in FIG. 6 corresponds to a sample in which there is designed for the substrate to be as 450 μm, meanwhile, a straight line (R6) therein corresponds to another sample in which there is designed for the substrate to be as 625 μm on the contrary thereto. And then there is having a proportional connection for between the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof and the amount of curvature of each of the substrates as shown by making use of the individual straight lines in FIG. 6. Furthermore, there is having the proportional connection for between the Lattice strain in the DBR mirror at the lower side thereof and the composition of nitrogen to be added into such the DBR mirror at the lower side thereof as shown in FIG. 5. And therefore there is performed the evaluation for the value of the lower limit at which there is not suppressed the occurrence of any dislocation therein in each of the above descriptions by assuming that the relation of between the Lattice strain in the DBR mirror at the lower side thereof and the amount of curvature of the substrate as shown in FIG. 4 is the proportional connection, as there is no problem at all in particular and it is appropriate for assuming that the relation of between the Lattice strain in the DBR mirror at the lower side thereof and the amount of curvature of the substrate is the proportional connection as well, because there becomes to be the proportional connection for both of the relation of between the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof and the amount of curvature of the substrate and the relation of between the average of the composition of the nitrogen at the inner side of the DBR mirror at the lower side thereof and the amount of curvature of the substrate.

The Second Embodiment

Next, the second embodiment in accordance with the present invention will be described in detail below. FIG. 7 is a cross sectional view for showing a schematic configuration regarding a principal part of a vertical cavity surface emitting laser element in accordance with the second embodiment. Moreover, such the vertical cavity surface emitting laser element in accordance with the second embodiment also has a planar configuration as similar to that in accordance with FIG. 1. Further, a vertical cavity surface emitting laser element (200) in accordance with the second embodiment comprises a configuration in which there is provided a DBR mirror at a lower side thereof (202) as shown in FIG. 7, that is in place of the DBR mirror at the lower side thereof (2) in accordance with the vertical cavity surface emitting laser element (100) as shown in FIG. 2. Still further, in accordance with such the DBR mirror at the lower side thereof (202), there is designed to be added not nitrogen but phosphorus (P) thereinto, that has a function to decrease a lattice constant thereof as similar to that with making use of nitrogen therefor. Still further, there is designed for a Lattice strain in the DBR mirror at the lower side thereof (202) to be as within a range by which it is possible to suppress an occurrence of any dislocation therein by performing a control of an amount of an addition of phosphorus that has the function to decrease the lattice constant thereof in accordance with the second embodiment.

Still further, there is performed an evaluation for an amount of a curvature of a substrate by which there is not occurred any dislocation therein in accordance with the second embodiment as similar to that in accordance with the first embodiment. And then there is designed to be set for the Lattice strain in the DBR mirror at the lower side thereof (202) and for a total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof (202) in order to realize such the amount of the curvature of a substrate. That is to say, it becomes able to design for the Lattice strain in the DBR mirror at the lower side thereof and for the total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof to be set individually as properly in accordance with the second embodiment as similar to that in accordance with the first embodiment, by designing to be set individually for the Lattice strain in the DBR mirror at the lower side thereof and for the total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof by making use of the formula (8) which is expressed above, for the amount of the curvature of the substrate (C) in order to satisfy the formula (9).

And then in order to design to be set for the Lattice strain in the DBR mirror at the lower side thereof (202) that satisfies the amount of the curvature of the substrate (C) by which there is not occurred any dislocation therein, there is designed for a range of the composition of phosphorus to be added into a layer having an index of refraction as lower or into a layer having an index of refraction as higher that configure the DBR mirror at the lower side thereof with following a description as below.

Still further, it is able to perform an evaluation as theoretically as similar to the case for the nitrogen therein in accordance with the first embodiment regarding a relation of between the composition of phosphorus to be added into such the DBR mirror at the lower side thereof and the Lattice strain in such the DBR mirror at the lower side thereof. Here there is shown in FIG. 8 as more specifically thereto regarding such the relation of between a Lattice strain in a DBR mirror at a lower side thereof and a composition of phosphorus to be added into such the DBR mirror. Still further, there is shown in accordance with FIG. 8 regarding a case where there is performed an arithmetic execution of the Lattice strain in the DBR mirror at the lower side thereof in a case where there is performed an addition of phosphorus that has each of compositions into the layer of AlAs which configures the layer having the index of refraction as lower in the DBR mirror at the lower side thereof, and then where there is made an estimation of the composition of the phosphorus at an inner side of the DBR mirror at the lower side thereof by making use of a ratio of between a thickness of the layer at the lower side thereof having the index of refraction as higher and a thickness of the layer at the lower side thereof having the index of refraction as lower.

Still further, there is having a proportional connection as theoretically for between the Lattice strain in the DBR mirror thereat and an average of the composition of the phosphorus at the inner side of such the DBR mirror thereat as shown by making use of a straight line (R7) in FIG. 8, and then thereby it is able to express such the relation thereof by making use of the following formula (11). Still further, there is defined for an average of strain in a DBR mirror at a lower side thereof in accordance with the formula (11) here to be as (S) (%), and there is defined for an average of a composition of phosphorus at an inner side of the DBR mirror at the lower side thereof therein here to be as (P) (%).

[Formula (11)]

P=−14.578S+2.0113  (11)

Still further, there is designed a total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof and the Lattice strain therein in accordance with the second embodiment by making use of the formula (8) which is expressed above, for the amount of the curvature in the substrate (C) in order to satisfy the formula (9) that is expressed above and that is the condition where there is not occurred any dislocation therein. Furthermore, there is designed for the phosphorus in accordance with the second embodiment to be included in the DBR mirror at the lower side thereof as uniformly in accordance with the formula (11) that is expressed above, with a composition that corresponds to the average strain in the DBR mirror at the lower side thereof which is designed to be set by making use of the formula (8) which is expressed above. And therefore it becomes able to suppress the occurrence of any dislocation therein in accordance with the second embodiment by designing an average of a composition of phosphorus that becomes to be included in the DBR mirror at the lower side thereof, by making use of the formula (8), the formula (9) and the formula (11) that are expressed above.

Here in a case where there is selected a sample substrate in actual in which a thickness of the substrate is determined to be as approximately 450 μm and a diameter of the substrate is determined to be as approximately 3 inches for instance, there becomes to be performed an evaluation for a range of the amount of the curvature of the substrate (C) at which there is not occurred any dislocation therein to be as −61.5 μm<C<61.5 μm by making use of the formula (9) that is expressed above. And then thereby in a case where there is further designed for a total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof to be as approximately 6.09 μm for instance, there becomes to be performed an evaluation for a range of the Lattice strain (S) in order to satisfy such the amount of the curvature of the substrate (C) to be as −0.020%<S<0.126% by making use of the formula (8) that is expressed above.

And hence it becomes able to perform an evaluation for the average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof to be as higher than 0.169% but lower than 2.309% by making use of the formula (11) which is expressed above, that corresponds to the above mentioned range of the Lattice strain (S) in such the DBR mirror therein. Moreover, it becomes able to suppress the occurrence of any dislocation therein in accordance with the second embodiment by performing the addition of phosphorus into the DBR mirror at the lower side thereof (202) as uniformly within such the range of higher than 0.169% but lower than 2.309%. Further, it may be available to perform the addition of phosphorus into the layer of AlAs that configures the layer having the index of refraction as lower in the DBR mirror at the lower side thereof (202) within a range of higher than 0.338% but lower than 4.621% for instance, without performing any addition of phosphorus into the layer of GaAs that configures the layer having the index of refraction as higher in the DBR mirror at the lower side thereof (202), in order to perform the addition of phosphorus as uniformly into the DBR mirror at the lower side thereof (202) within such the above mentioned range of higher than 0.169% but lower than 2.309%.

And therefore it becomes possible to realize as simply the vertical cavity surface emitting laser element that there is designed as properly for suppressing the occurrence of any dislocation therein and then that has the reliability as higher in accordance with the second embodiment as similar to that in accordance with the first embodiment, by designing to be set the total of the layer thicknesses of the film layers in the DBR mirror at the lower side thereof and the Lattice strain therein by making use of the formula (8) which is expressed above, for the amount of the curvature in the substrate (C) in order to satisfy the formula (9) that is expressed above and that is the condition where there is not occurred any dislocation therein, and then by performing the addition of phosphorus into the DBR mirror at the lower side thereof with the composition thereof that is performed to be evaluated by making use of the formula (11) which is expressed above and that corresponds to the average of strain in the DBR mirror at the lower side thereof which is designed to be set by making use of the formula (8) that is expressed above.

Moreover, it may be available to perform further the control of the amount of phosphorus to be added into the DBR mirror at the lower side thereof as well in accordance with the present second embodiment as similar to that in accordance with the first embodiment, by taking into consideration of an amount of the curvature of the substrate that increases due to a process of an accumulation of an active layer of a compressive strain onto such the DBR mirror at the lower side thereof.

Further, there is performed an evaluation as more specifically thereto for the Lattice strain therein as (S₁) to be as 0.072% that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto as similar to that in accordance with the first embodiment, by making use of the value of the lower limit for the Lattice strain therein as −0.0195% and the total of the layer thicknesses of the film layers in the DBR mirror thereat as 6.09 μm for instance, with assuming the amount of the curvature of the substrate to be as approximately 15 μm that is the increased amount in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof. And then such the Lattice strain therein as (S₁) becomes to be determined as an amount of a lower value for the Lattice strain therein that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto. Still further, there becomes to be as 0.410% by making use of the formula (11) for an average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof which corresponds to 0.072% as the value of the lower limit for the Lattice strain therein that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto. Still further, the value of the upper limit for the average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof at which there is not occurred any dislocation therein is here 2.29% that is performed the evaluation as above. And then thereby in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (202), it becomes to be required for the average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof to be designed as between 0.410% and 2.29% in order to suppress the occurrence of any dislocation therein. That is to say, in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (202), it becomes to be required for the average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof to be designed as not lower than 0.410% in order to suppress the occurrence of any dislocation therein. Furthermore, regarding a condition for dislocation free in a case where there is designed to be performed an accumulation of an active layer of a tensile strain thereunto, the strain of the DBR becomes to be dominant therein, and hence there becomes not to be occurred any variation thereby regarding the value of the lower limit for the composition thereof.

Moreover, it may be available to perform further the control of the amount of phosphorus to be added into the DBR mirror at the lower side thereof as well in accordance with the present second embodiment as similar to that in accordance with the first embodiment, by taking into consideration of an amount of the curvature of the substrate that increases due to a further process of an accumulation of a DBR mirror at an upper side thereof onto the active layer therein later.

Further, there is performed an evaluation as more specifically thereto for the Lattice strain therein as (S₂) to be as 0.263% that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto and then due to the accumulation of the DBR mirror at the upper side thereof as similar to that in accordance with the first embodiment, by making use of the value of the lower limit for the Lattice strain therein as −0.020% and the total of the layer thicknesses of the film layers in the DBR mirror thereat as 6.09 μm for instance, with assuming the amount of the curvature of the substrate to be as approximately 80 μm that is the increased amount in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof and then there is performed thereunto the accumulation of the DBR mirror at the upper side thereof. And then such the Lattice strain therein as (S₂) becomes to be determined as an amount of a lower value for the Lattice strain therein that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto and then due to the accumulation of the DBR mirror at the upper side thereof. Still further, there becomes to be as 1.551% by making use of the formula (11) for an average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof which corresponds to 0.263% as the value of the lower limit for the Lattice strain therein that corresponds to the increase of the amount of the curvature of the substrate due to the accumulation of the active layer thereunto and then due to the accumulation of the DBR mirror at the upper side thereof. Furthermore, the value of the upper limit for the average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof at which there is not occurred any dislocation therein is here 2.29% that is performed the evaluation as above. And then thereby in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (202) and then there is performed thereunto the accumulation of the DBR mirror at the upper side thereof, it becomes to be required for the average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof to be designed as between 1.551% and 2.29% in order to suppress the occurrence of any dislocation therein. That is to say, in the case where there is performed the accumulation of the active layer onto the DBR mirror at the lower side thereof (202) and then there is performed thereunto the accumulation of the DBR mirror at the upper side thereof, it becomes to be required for the average of the composition of the phosphorus at the inner side of the DBR mirror at the lower side thereof to be designed as not lower than 1.551% in order to suppress the occurrence of any dislocation therein.

Moreover, there are described with giving the example of the vertical cavity surface emitting laser element in which the active layer (6) is formed with making use of the material of GaInNAs system and that has the wavelength of emission therefrom with having the band of 1.3 μm in accordance with each of the first and the second embodiments. However, it is possible to select as properly a wavelength of emission from such the vertical cavity surface emitting laser element or a material therein that configures such as an active layer or the like. And then it is possible to select either one of a material of AlGaInP system or a material of InGaAsP system for a vertical cavity surface emitting laser element that has a wavelength of emission therefrom with having a band of 650 nm for instance, or it is possible to select a material of InGaAs system for another vertical cavity surface emitting laser element that has another wavelength of emission therefrom with having a band of 1 μm for instance, or it is possible to select any one of a material of GaInAsP system or a material of AlGaInP system or a material of GaInNAsSb system for another vertical cavity surface emitting laser element that has another wavelength of emission therefrom with having a band of between 1.3 μm and 1.6 μm for instance.

Further, there are described with giving the example of the case where there is designed for the whole of the DBR mirror at the upper side thereof (12) to be comprised of the film layers of the dielectric substance in accordance with each of the first and the second embodiments. However, there is no problem at all for a part of such the DBR mirror at the upper side thereof (12) to be comprised of the film layers of the dielectric substance, meanwhile, for the other parts thereof to be comprised of a film layer of a semiconductor on the contrary thereto, or there is no problem at all for the whole thereof to be comprised of a film layer of a semiconductor as well. Still further, there are described with giving the example of the case where there is designed for the film layers of the dielectric substance that individually configure the DBR mirror at the upper side thereof (12) to be formed with making use of the composite layer of the dielectric substance that is comprised of such as the SiN/SiO₂ or the like in accordance with each of the first and the second embodiments. However, it is not necessary to interpret at all with limiting any material for the film layer to such the material. And then it is able to make use of any one which is selected from such as SiO₂ or SiN or a-Si or AlO or MgF or ITO or TiO or the like with being combined together with each other as properly therefor. Still further, it is possible to form SiO₂ SiN and a-Si in general by making use of an equipment of a plasma CVD method, or it is possible to form SiO₂, a-Si, AlO, MgF, ITO and TiO by making use of an equipment of an electron beam evaporation method, or it is possible to form SiO₂, a-Si, AlO and ITO by making use of an equipment of a spattering method.

Furthermore, there are described as above with giving the examples of the vertical cavity surface emitting laser elements (100) and (200) in accordance with the first and the second embodiments respectively, however, it is possible without any problem at all to apply each of such the embodiments to an array of the vertical cavity surface emitting laser elements in which either one type of such the vertical cavity surface emitting laser elements (100) or (200) are designed to be arrayed in one dimensional or either one type of such the elements are designed to be arrayed in two dimensional as well.

Although the invention has been described with respect to specific embodiments for a complete and clear disclosure, appended claims are not to be thus limited but are to be construed as embodying all modifications and alternative constructions that may occur to one skilled in the art that fairly fall within the basic teaching herein set forth. 

1. A vertical cavity surface emitting laser element, comprising: a substrate; a reflecting mirror of a multilayered film layer at a lower side thereof, that is formed on the substrate by making use of a periodic structure of between a layer at a lower side thereof having an index of refraction as higher which is formed by making use of a chemical compound which includes Ga and As, and a layer at a lower side thereof having an index of refraction as lower which is formed by making use of a chemical compound which includes Al and As; an optical resonator which comprises a reflecting mirror of a multilayered film layer at an upper side thereof, that is formed by making use of a periodic structure of between a layer at an upper side thereof having an index of refraction as higher and a layer at an upper side thereof having an index of refraction as lower; and an active layer, that is provided in between the reflecting mirror of the multilayered film layer at the lower side thereof and the reflecting mirror of the multilayered film layer at the upper side thereof, and that generates a light emission, wherein there is included a nitrogen in the reflecting mirror of the multilayered film layer at the lower side thereof, there is designed to be set for between an average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof and a layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof in reference to the following formula (2) for a curvature of the substrate to be satisfied with the following formula (1) in a case where the curvature of the substrate is defined here to be as (C) (μm), the average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (S) (%), a thickness of the substrate is defined to be as (d) (μm), a diameter of the substrate is defined to be as (D) (inch), and the layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (T) (μm), and there is included the nitrogen in the reflecting mirror of the multilayered film layer at the lower side thereof with having a composition which corresponds to the average of strain (S) by designing to be set with making use of the formula (2) in accordance with a relationship between the average of strain and an average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof. [Formula  (1)] $\begin{matrix} {{C} < {61.5 \times \left( \frac{450}{d} \right)^{2} \times {\left( \frac{D}{3} \right)^{2}\left\lbrack {{Formula}\mspace{14mu} (2)} \right\rbrack}}} & (1) \\ {C = {\frac{\left( {{27.7S} - 1.48} \right)}{0.2} \times \left( \frac{450}{d} \right)^{2} \times \left( \frac{D}{3} \right)^{2} \times T}} & (2) \end{matrix}$
 2. The vertical cavity surface emitting laser element as defined in claim 1, wherein the relationship between the average of strain and the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is expressed by making use of the following formula (3) in a case where the average of composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is defined to be as (N). [Formula (3)] N=−2.4756S+0.3409  (3)
 3. The vertical cavity surface emitting laser element as defined in either one of claim 1 or 2, wherein there is designed for the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as between 0.028% and 0.390%.
 4. The vertical cavity surface emitting laser element as defined in claim 3, wherein there is designed for the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 0.072%.
 5. The vertical cavity surface emitting laser element as defined in claim 3, wherein there is designed for the average of the composition of the nitrogen which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 0.263%.
 6. A vertical cavity surface emitting laser element, further comprising: a substrate; a reflecting mirror of a multilayered film layer at a lower side thereof, that is formed on the substrate by making use of a periodic structure of between a layer at a lower side thereof having an index of refraction as higher which is formed by making use of a chemical compound which includes Ga and As, and a layer at a lower side thereof having an index of refraction as lower which is formed by making use of a chemical compound which includes Al and As; an optical resonator which comprises a reflecting mirror of a multilayered film layer at an upper side thereof, that is formed by making use of a periodic structure of between a layer at an upper side thereof having an index of refraction as higher and a layer at an upper side thereof having an index of refraction as lower; and an active layer, that is provided in between the reflecting mirror of the multilayered film layer at the lower side thereof and the reflecting mirror of the multilayered film layer at the upper side thereof, and that generates a light emission, wherein there is included a phosphorus in the reflecting mirror of the multilayered film layer at the lower side thereof, there is designed to be set for between an average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof and a layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof in reference to the following formula (5) for a curvature of the substrate to be satisfied with the following formula (4) in a case where the curvature of the substrate is defined here to be as (C) (μm), the average of strain of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (S) (%), a thickness of the substrate is defined to be as (d) (μm), a diameter of the substrate is defined to be as (D) (inch), and the layer thickness of the reflecting mirror of the multilayered film layer at the lower side thereof is defined here to be as (T) (μm), and there is included the phosphorus in the reflecting mirror of the multilayered film layer at the lower side thereof with having a composition which corresponds to the average of strain (S) by designing to be set with making use of the formula (5) in accordance with a relationship between the average of strain and an average of the composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof. [Formula  (4)] $\begin{matrix} {{C} < {61.5 \times \left( \frac{450}{d} \right)^{2} \times {\left( \frac{D}{3} \right)^{2}\left\lbrack {{Formula}\mspace{14mu} (5)} \right\rbrack}}} & (4) \\ {C = {\frac{\left( {{27.7S} - 1.48} \right)}{0.2} \times \left( \frac{450}{d} \right)^{2} \times \left( \frac{D}{3} \right)^{2} \times T}} & (5) \end{matrix}$
 7. The vertical cavity surface emitting laser element as defined in claim 6, wherein the relationship between the average of strain and the average of composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is expressed by making use of the following formula (6) in a case where the average of composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof is defined to be as (P). [Formula (6)] P=−14.578S+2.0113  (6)
 8. The vertical cavity surface emitting laser element as defined in either one of claim 6 or 7, wherein there is designed for the average of composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as between 0.169% and 2.309%.
 9. The vertical cavity surface emitting laser element as defined in either one of claim 6 or 7, wherein there is included the phosphorus in the layer at the lower side thereof having the index of refraction as lower in the reflecting mirror of the multilayered film layer at the lower side thereof, and there is designed for the composition of the phosphorus which is included in the layer at the lower side thereof having the index of refraction as lower to be as between 0.338% and 4.621%.
 10. The vertical cavity surface emitting laser element as defined in claim 8, wherein there is designed for the average of the composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 0.410%.
 11. The vertical cavity surface emitting laser element as defined in claim 8, wherein there is designed for the average of the composition of the phosphorus which is included in the reflecting mirror of the multilayered film layer at the lower side thereof to be as not less than 1.551%. 